\newproblem{lay:7_2_5}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 7.2.5}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Find the matrix of the quadratic form. Assume $\mathbf{x}$ is in $\mathbb{R}^3$.
	\begin{enumerate}[a.]
		\item $Q(\mathbf{x})=8x_1^2+7x_2^2-3x_3^2-6x_1x_2+4x_1x_3-2x_2x_3$
		\item $Q(\mathbf{x})=4x_1x_2+6x_1x_3-8x_2x_3$
	\end{enumerate}
}{
   % Solution
	We look for the matrix $A$ such that $Q(\mathbf{x})=\mathbf{x}^TA\mathbf{x}$. It can be easily verified that the solution of this
	problem is 
	\begin{enumerate}[a.]
		\item $A=\begin{pmatrix}8 & -3 & 2 \\ -3 & 7 & -1 \\ 2 & -1 & -3 \end{pmatrix}$
		\item $A=\begin{pmatrix}0 & 2 & 3 \\ 2 & 0 & -4 \\ 3 & -4 & 0 \end{pmatrix}$
	\end{enumerate}
}
\useproblem{lay:7_2_5}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}

